Sounds like you need to work on some things, OP.
Trigger discipline is the big one. There are so many indicators as to where ships are around you.
Your scanner is probably the most obvious of them but there are other things to look out for such as: the sounds other ships make when they're close to you, the direction approaching ships fire is coming from, as well as your good old fashion visual implants v1.0 (eyes).
It'll get better with practice. If you suspect another ship is going to fly through your field of fire, hold off on the trigger for a second to see where they're going.
As for being blasted trying to dock with a bounty on your head, that too comes with practice.
There's a few ways you can go about that. The easiest is probably just to manually shut down all systems except for sensors and thrusters at around the distance you can request docking. Keep an eye out for circling patrol ships near the docking slot and fly as fast as you can through the slot. There's a lot of ways to sneak in, just look on YouTube for ideas. Or you could skip big stations all together. Since you can pay a bounty off from anywhere in the galaxy, why not try an outpost or a station owned by a faction that doesn't have you on their KOS list? It doesn't even have to be in the same system as the faction that initially tagged you as wanted.
Just my 2c.
Practice, practice, practice, my friend. It'll get easier.